Answer :

Let ABCD be rhombus.



We know that rhombus is type of parallelogram whose all sides are equal.


AB = BC = CD = DA = 10 cm


Let the diagonals AC and BD intersect each other at O, where AC = 16 cm and let BD = x
We know that the diagonals of a rhombus are perpendicular bisectors of each other.
AOB is a right angle triangle, in which OB = BD ÷ 2 = x ÷ 2 and OA = AC ÷2 = 16 ÷ 2 = 8 cm.
Now, AB= OA2 + OB2…by pythagoras theorem
102 = ( )2 + 82


ie. 100 64 =


36 ×4 = x2
x2 =144
x = 12 cm


Hence, the length of the other diagonal is 12 cm


We know that area of rhombus is,


Area of rhombus = × ( Diagonal1) × ( Diagonal2)


Hence,


Area of ABCD = × AC × BD


= × 16 × 12


= 96 cm2


Hence, the area of rhombus is 96 cm2


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